How do you solve the inequality #|2x+3| > |x- 4|#? Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities 1 Answer Cesareo R. Feb 26, 2017 #x < -7# or #x > 1/3# Explanation: #|2x+3| > |x- 4|# supposing #x ne 4# we have #abs((2x+3)/(x-4)) > 1# or equivalently #-1 < (2x+3)/(x-4) < 1# or #-x+4 < 2x + 3->x > 1/3# or #2x+3 < x-4->x < -7# The feasible #x# are: #x < -7# or #x > 1/3# Answer link Related questions How do you solve absolute value inequalities? When is a solution "all real numbers" when solving absolute value inequalities? How do you solve #|a+1|\le 4#? How do you solve #|-6t+3|+9 \ge 18#? How do you graph #|7x| \ge 21#? Are all absolute value inequalities going to turn into compound inequalities? How do you solve for x given #|\frac{2x}{7}+9 | > frac{5}{7}#? How do you solve #abs(2x-3)<=4#? How do you solve #abs(2-x)>abs(x+1)#? How do you solve this absolute-value inequality #6abs(2x + 5 )> 66#? See all questions in Absolute Value Inequalities Impact of this question 2532 views around the world You can reuse this answer Creative Commons License